1. Boolean Algebra

2. Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the late 1830s. It created a notation for Aristotle's system of logic George Boole (1815 – 1864) Aristotle (384 BC – 322 BC)

3. The Basics Boolean algebra works on variables having only two states; generally represented as True or False. “Mr Williams is happy” is a true or false statement and so could be represented by the variable X rather than using T or F, we tend to use 1 and 0 X True (1)Mr Williams is happy False (0)Mr Williams is not Happy

4. AND function (conjunction ٨) Mr Williams is happy (X) It is hot (Y) Mr Williams is happy and it is hot (Q) We represent AND with a dot X.Y = Q (x ٨ y=q) Truth table for AND XYQ 00 01 10 11

5. OR function (disjunction ٧) We represent OR with a + X+Y = Q (x ٧ y=q) Truth table for OR XYQ 00 01 10 11

6. NOT function (negation ¬) The NOT function inverts the input Q=X XQ 0 1 ¬x

7. Commutative Laws A+B =B+A A.B = B.A The order of the statements in an OR / AND does not change the outcome. Mr Williams is happy and the sun is out The sun is out and Mr Williams is happy

8. Tautology Laws A.A =? A+A = ? A.A=? AQ 0 1 AAQ 0 1 AAQ 0 1

9. A+(A.B) =? ABA.BQ 00 01 10 11

10. A.(A+B)= ABA+BQ 00 01 10 11